scholarly journals On Accuracy of Analytical Modeling of Lamb Wave Scattering at Delaminations in Multilayered Isotropic Plates

2015 ◽  
Vol 15 (08) ◽  
pp. 1540010 ◽  
Author(s):  
C. T. Ng
Keyword(s):  
Analytical Solutions ◽  
Lamb Wave ◽  
Wave Scattering ◽  
Plate Theory ◽  
Analytical Models ◽  
Mindlin Plate ◽  
Bending Rigidity ◽  
Scattering Problems ◽  
Explicit Finite Element ◽  
Isotropic Plates

The study investigates the accuracy of analytical solutions to the fundamental anti-symmetric Lamb wave scattering at delamination in multilayered isotropic plates. The analytical models are based on the wave function expansion method and Born approximation within the framework of Mindlin plate theory. The study validates the accuracy of modeling the delamination as an inhomogeneity with reduced bending rigidity in predicting Lamb wave scattering induced by geometry change at the delaminated region. A good agreement is observed between the analytical solutions and results of experimentally verified 3D explicit finite element (FE) simulations. The findings support the inhomogeneity assumption in Lamb wave scattering problems and show the feasibility of employing it in delamination characterization.

Scattering of Lamb Waves by a Cylindrical Mass Attached to the Surface of a Plate

2016 ◽  
Author(s):  
Andrew Golato ◽  
Sridhar Santhanam ◽  
Fauzia Ahmad ◽  
Moeness G. Amin
Keyword(s):  
Lamb Wave ◽  
Lamb Waves ◽  
Plate Theory ◽  
Wave Mode ◽  
Guided Wave ◽  
Potential Functions ◽  
Mindlin Plate ◽  
Detection Scheme ◽  
Linear System Of Equations ◽  
Scattering Response

Defect classification is the logical next step after localization in a Lamb wave based Guided Wave Structural Health Monitoring (GWSHM) defect detection scheme. Lamb waves are a preferred wave mode in GWSHM; therefore, classification can be facilitated via understanding of the Lamb wave scattering characteristics of defects. Many defects can be modeled either as (part-) through holes or accumulated masses on the surface. We consider and analytically solve the scenario of an attached mass on the surface of a plate. The mass is treated as an elastic isotropic homogeneous cylinder and the scattering response is obtained for incident fundamental symmetric and antisymmetric waves. Propagation is modeled via Mindlin plate theory, utilizing infinite series of Bessel functions as potential functions. Boundary and continuity conditions provide a linear system of equations for the expansion coefficients of the potential functions, which, solved numerically, produce the scattering response of the defect.

Uniform Horizontal Groundwater Flow against Dispersion in a Shallow Aquifer: Two Analytical Models

1992 ◽  
Vol 23 (1) ◽  
pp. 1-12
Author(s):  
Ram Raj Vinda ◽  
Raja Ram Yadava ◽  
Naveen Kumar
Keyword(s):  
Point Source ◽  
Groundwater Flow ◽  
Cross Section ◽  
Analytical Solutions ◽  
Concentration Distribution ◽  
Analytical Models ◽  
Shallow Aquifer ◽  
Horizontal Cross Section ◽  
Flow Components ◽  
Reactive Pollutant

Analytical solutions converging rapidly at large and small values of times have been obtained for two mathematical models which describe the concentration distribution of a non reactive pollutant from a point source against the flow in a horizontal cross-section of a finite saturated shallow aquifer possessing uniform horizontal groundwater flow. Zero concentration or the conditions in which the flux across the extreme boundaries are proportional to the respective flow components are applied. The effects of flow and dispersion on concentration distribution are also discussed.

scholarly journals Lamb Wave Scattering Analysis for Interface Damage Detection between a Surface-Mounted Block and Elastic Plate

Sensors ◽  
2021 ◽  
Vol 21 (3) ◽  
pp. 860
Author(s):  
Mikhail V. Golub ◽  
Alisa N. Shpak ◽  
Inka Mueller ◽  
Sergey I. Fomenko ◽  
Claus-Peter Fritzen
Keyword(s):  
Damage Detection ◽  
Elastic Plate ◽  
Lamb Wave ◽  
Wave Scattering ◽  
Hybrid Approach ◽  
Guided Wave ◽  
Open Crack ◽  
Damage Indices ◽  
Impulse Function ◽  
Thin Walled

Since stringers are often applied in engineering constructions to improve thin-walled structures’ strength, methods for damage detection at the joints between the stringer and the thin-walled structure are necessary. A 2D mathematical model was employed to simulate Lamb wave excitation and sensing via rectangular piezoelectric-wafer active transducers mounted on the surface of an elastic plate with rectangular surface-bonded obstacles (stiffeners) with interface defects. The results of a 2D simulation using the finite element method and the semi-analytical hybrid approach were validated experimentally using laser Doppler vibrometry for fully bonded and semi-debonded rectangular obstacles. A numerical analysis of fundamental Lamb wave scattering via rectangular stiffeners in different bonding states is presented. Two kinds of interfacial defects between the stiffener and the plate are considered: the partial degradation of the adhesive at the interface and an open crack. Damage indices calculated using the data obtained from a sensor are analyzed numerically. The choice of an input impulse function applied at the piezoelectric actuator is discussed from the perspective of the development of guided-wave-based structural health monitoring techniques for damage detection.

Coupled Extensional and Flexural Motions of a Two-Layer Plate With Interface Slip

2018 ◽  
Vol 141 (2) ◽  
Author(s):  
Peng Li ◽  
Feng Jin ◽  
Weiqiu Chen ◽  
Jiashi Yang
Keyword(s):  
Plate Theory ◽  
Cutoff Frequency ◽  
Great Influence ◽  
Imperfect Interface ◽  
Mindlin Plate ◽  
Finite Plate ◽  
Mindlin Plate Theory ◽  
Interface Elasticity ◽  
Propagating Shear ◽  
Perfect Interface

The effect of imperfect interface on the coupled extensional and flexural motions in a two-layer elastic plate is investigated from views of theoretical analysis and numerical simulations. A set of full two-dimensional equations is obtained based on Mindlin plate theory and shear-slip model, which concerns the interface elasticity and tangential discontinuous displacements across the bonding imperfect interface. Some numerical examples are processed, including the propagation of straight-crested waves in an unbounded plate, the buckling of a finite plate, as well as the deflection of a finite plate under uniform load. It is revealed that the bending-evanescent wave in the composites with a perfect interface eventually cuts-on to a propagating shear-like wave with cutoff frequency when the two sublayers imperfectly bonded. The similar phenomenon has been verified once again for coupled face-shear and thickness-shear waves. It also has been pointed out that the interfacial parameter has a great influence on the performance of static buckling, in which the outcome can be reduced to classical buckling load of a simply supported plate when the interface is perfect.

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